Locomotion on rough unknown terrain has been a major challenge for legged robotic systems. Hexapods offer the advantage of static stability due to their capability of maintaining their center of gravity within their support polygon. Various approaches have been proposed for moving on rough terrain that use mapping of the ground or control schemes that result to discontinuous or oscillating motion of the hexapod body. In these approaches, stability is not taken into account, and increased tip-over risk occurs. This work presents a novel approach for continuous and smooth locomotion of a hexapod on rough terrain while maintaining static stability at predefined values regardless of the terrain profile and the existence of obstacles and slopes. The locomotion of the body is adjusted through a correction algorithm that facilitates smooth body motion following the variation of the terrain while static stability is maintained. The effect of the body correction algorithm gains on the body motion behavior with respect to terrain variation is thoroughly analyzed and the approach is evaluated using the force-angle stability measure. Results using multibody dynamics simulations show the effectiveness of the developed approach.